As frustration grows among hard-line immigration policy advocates, Trump admin officials say they must follow court orders or risk being held in contempt

This was supposed to be the week that former President Barack Obama’s quasi-amnesty program for illegal immigrants ended. Instead, the Department of Homeland Security (DHS) said Wednesday it has begun processing applications for renewals.

“We note that the DACA protections currently in place due to a court injunction are the result of a likely unconstitutional exercise of executive authority and only good for two years at a time,” Houlton said in a statement.

That is little comfort to DACA’s harshest critics, since the program offers authorization to work in the United States and protection from deportation to illegal immigrants brought to America as children by their parents. Obama created DACA though an executive order in 2012 after Congress failed to pass an amnesty bill. Some 690,000 illegal immigrants currently are enrolled.

William Gheen, president of the Americans for Legal Immigration Political Action Committee (ALIPAC), urged Trump to end the program, courts be damned.

"Donald Trump should end DACA immediately and let judges complain," he said. "Every moment DACA continues, the United States is under martial law."

Two different judges, U.S. District Judge William Alsup in San Francisco and U.S. District Judge Nicholas Garaufis in Brooklyn, New York, have issued rulings that Trump likely failed to follow required procedures in rescinding DACA. The Supreme Court last month declined a request to intervene quickly in the dispute.

That means the cases will proceed on a standard timeline, with appellate courts weighing in before the Supreme Court hears the cases. Andrew Arthur, senior fellow in law and policy at the Center for Immigration Studies (CIS), predicted the justices will not get the case until the next term.

Until then, DHS will have to process the applications for DACA renewals. "They don't have a choice," he said.

Arthur said any action that deviates from the orders issued by the federal judges carries great risk.

"The problem is if you violate the order, you're in contempt," he said.

Gheen, whose organization retroactively rescinded its 2016 endorsement of Trump because he broke his campaign promise to revoke DACA immediately upon taking office, said the president has left no doubt about his views.

"Trump has made it clear he wants DACA," Gheen said. "His head of DHS had made it clear she wants DACA."

Trump earlier this year dangled the prospect of amnesty not just for the DACA enrollees but for a grand total of 1.8 million similarly situated young adults. But Democrats balked at changes to the legal immigration system that Trump required as part of a deal.

Trump said Wednesday he remains "ready, willing and able" to agree to amnesty.

"We are trying to have a DACA victory for everybody," he told the Latino Coalition Legislative Summit in Washington, according to Fox News. "And the Democrats are nowhere to be found. They are nowhere to be found."

United We Dream, an advocacy organization that favors amnesty, accused Trump Wednesday of "sabotaging" legislative efforts: "Instead of becoming citizens, immigrant youth are being hunted."

But DHS spokesman Houlton said in his statement that "absent additional negative factors, DACA recipients are not a priority or target group for arrest or removal."

He added that DACA enrollees will not be targeted unless they pose a threat to public safety or national security.